Question

if x>y and z>w then x+z>y+w. Prove it

Answer 1

Another way you can look at it would be
since x > y
x + z > y or any variable you put in place for z will always be greater than y
as well as z > w
x + z > w or any variable you put in place for x will always be greater than y
so this just states
x + z > y + w
since both values are greater.
I'm not sure how much that helps, but it is a different way to look at it

that is what i posted for someone asking the same question. Hope it helps.

Answer 2

x>y add z to both sides

x+z>y+z

and we know z>w so

x+z>y+z>y+w

we are done